Hi There, if your project is all finished all you need is the actual project file and all the raw files that make up your project. You don't need to move the scratch files. Premiere will recreate them when you open the project on the laptop.
Basically move everything and then open the project ( it might be an idea to make a copy of the project first and then open that file), Premiere will ask you to relink all the media that was used by browsing to it's new location. You won't have to do this for every single file. If multiple files are in the same folder premiere will see them and relink them itself. If it asks you for the location of a long filename that you don't recognise it's probably a preview file. You can hit the "skip preview files" buttons and rebuild them later if you really need to.
Once premiere actually opens it will need to conform the audio and build pek files.
Let it do that and then look in your sequences to make sure none of the files are offline. If any are you can right click on them, select reveal in project, that clip will be highlighted in the project window and then you can right click and select "link media" to browse to the clip location.
Once you get to that point you should be able to export your sequence.
Hope that helps, if not reply here and I'll try and help.
Premiere will ask you to relink all the media
If you assign the external the same drive letter it had on your workstation, PP should just find the media and move along.
I agree with Jim. I migrate between a workstation and a laptop w/ external HDD's, containing the PRPROJ file and ALL Assets. I set the drive letter in the OS of both computers (in this case, the OP has but one computer), and PrPro always locates all Assets perfectly.
Good luck, and just go into the disc management area of your OS, to make that drive letter change, before firing up PrPro. Depending on your OS version, this might be accessed several ways, and it would probably be best to Search your OS's Help file for "drive letter," where you will likely get a link to the disc management console and instructions.